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Nonlinear Discriminant Analysis for Prediction of Failure Event in a Towing Tank Wavemaker

The MPR model was used to successfully develop a discriminant function to predict conditions that would cause system trips in a computer-controlled wavemaker machine used for nautical model testing.

The wavemaker received inputs in the form of position (x), velocity (v) and acceleration (a) for each of two hydraulically operated wavemaking rams, for a total of six inputs. However the system would "trip out" under certain situations. The operators could not identify what combinations of inputs caused trips. Several cases of trip-out conditions and similar conditions that did not cause trips were used as input data for modeling. The dependent variable was a coded pseudo-variable with a value of 1 for "caused a trip" and 0 for "did not trip". The program was able to identify a polynomial model discriminating between these cases.

The graph shows x, v and a for one of the test cases. The second figure shows a plot of the predicted discriminant variable versus time. The discriminant shows a sharp peak where the function reaches a value of 1.0, corresponding to the predicted time of the failure. When the inputs were used in the real wavemaker, the system caused a trip at exactly 16 seconds, just as predicted.

When the polynomial was used with newly generated test cases, it was successful in predicting both (a) which test cases would result in a trip, and (b) when the trip would actually occur.